The third stage of a typical gas turbine can have as many as 92 buckets that radially extend from a rotor or wheel. Each bucket has a root portion that is configured to mate with a corresponding broach slot in the wheel. The firtree/broach slot configurations are designed to reduce stresses that occur transiently and at normal operating speeds.
Prior known firtree/broach slot configurations are disclosed in Goodwin, U.S. Pat. No. 4,260,331 issued on Apr. 7, 1981, Pisz et al., U.S. Pat. No. 4,824,328 issued on Apr. 25, 1989, Dierksmeier et al., U.S. Pat. No. 5,688,108 issued on Nov. 18, 1997, Heppenstall, U.S. Pat. No. 5,741,119 issued on Apr. 21, 1998, Dierksmeier et al., U.S. Pat. No. 5,836,742 issued on Nov. 17, 1998, and Dierksmeier et al., U.S. Pat. No. 5,863,183 issued on Jan. 26, 1999. Each one of these prior art patents describes the particular details of the geometric assimilation of lines, arcs, and angles of its disclosed firtree/broach slot configuration for the purposes of reducing centrifugal forces, bending moments, and vibrations and the consequential peak stresses that result at the attachment points.
It is desirable to reduce the number of buckets to be attached to the wheel for a number of reasons, including fewer parts (less cost), higher natural frequencies, less profile losses (skin friction), and reduced overtip leakage. However, a reduction in the number of buckets also results in each individual bucket being heavier as it covers a longer circumferential length. Simply scaling the size of the buckets and slots on existing firtree and broach slot configurations, while maintaining the same size wheel, to reduce the number of buckets will not minimize the stresses acting at the attachment points.